resolve into factors x^13-x^12
Answers
Step-by-step explanation:
Answer
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Given
f(x)=x3−13x−12
To solve this type of problem, We have to find out at least one root by hit and trial using the factor theorem.
Here is a trick:
If a polynomial function has integer coefficients, then every rational zero will have the form qp, where p is a factor of the constant and q is a factor of the leading coefficient.
Here
p=±1,±2,±3,±4,±6,±12 and
q=±1
Find every combination of ±qp.
These are the possible roots of the polynomial function.
±1,±2,±3,±4,±6,±12
Substituting x=1 in f(x), we get
f(−1)=(−1)3−13(−1)12=−1+13−12=13+13=0
∴(x+1) is a factor of f(x)
Now, dividing f(x) by (x+1), we get
x3−13x−12=(x+1)(x2−x−12)
=(x+1)(x2−4x+3x−12)
=(x+1){x(x−4))+3(x−4)}
=(x+1)(x+3)(x−4)
Answer:
Step-by-step explanation:
Use factor theorem to factorize the following polynomials completely.
x
3
−13x−12
Answer
Given
f(x)=x
3
−13x−12
To solve this type of problem, We have to find out at least one root by hit and trial using the factor theorem.
Here is a trick:
If a polynomial function has integer coefficients, then every rational zero will have the form
q
p
, where p is a factor of the constant and q is a factor of the leading coefficient.
Here
p=±1,±2,±3,±4,±6,±12 and
q=±1
Find every combination of ±
q
p
.
These are the possible roots of the polynomial function.
±1,±2,±3,±4,±6,±12
Substituting x=1 in f(x), we get
f(−1)
=(−1)
3
−13(−1)12
=−1+13−12
=13+13
=0
∴(x+1) is a factor of f(x)
Now, dividing f(x) by (x+1), we get
x
3
−13x−12=(x+1)(x
2
−x−12)
=(x+1)(x
2
−4x+3x−12)
=(x+1){x(x−4))+3(x−4)}
=(x+1)(x+3)(x−4)